Question

Can anyone help me with the question please​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

7 a)

Step 1 :

Make the denominators the same

           $-\frac{1}{7} \ and \ \frac{2}{9}$

$-\frac{1}{7} \times \frac{9}{9} = -\frac{9}{63}\\\\\frac{2}{9} \times \frac{7}{7} = \frac{14}{63}$

Step 2 :

Now find rational between (-9/63) and (14/63).

Just change the number in the numerator. Write any numbers between -9 and 14 in the numerator.

                            $\frac{ -8}{63}, \ \frac{-7}{63},\ \frac{3}{63},\ \frac{6}{63},\ \frac{8}{63}$

7 b )

       $x = 3 + 2\sqrt2\\\\x + \frac{1}{x} = (3 + 2\sqrt2) + \frac{1}{3+2\sqrt2}$

$[ Rationalize \ the \ denominator : \frac{1}{3 + \sqrt2} \times \frac{3 - 2\sqrt2}{3-2\sqrt 2} = \frac{3 - 2 \sqrt2}{3^2 - (2 \sqrt2)^2 } = \frac{3 - 2\sqrt2}{9 - 8} = 3 - 2\sqrt 2 \ ]$

       $therefore , x + \frac{1}{x} = 3 + 2\sqrt 2 + 3 - 2 \sqrt 2 = 6 + 0 = 6$